Suppose that $~a~$ and $~b~$ are coprime positive integers. Then there exists representation of $~\frac{a}{b}~$ as egyptian fraction: $$~\frac{a}{b} = \frac{1}{d_1} + \cdots + \frac{1}{d_s} ~$$
There are many algorithms for constructing egyptian fraction of whic i know greedy algorithm mentioned in Wikipedia. Unfortunately it doesn't satisfy my needs. I'm searching for two algorithms which can construct representation with
a) shortest length
b) least sum of denominators
Any ideas will be highly appreciated. Thanks in advance.